Understanding FFT (Fast Fourier Transform)

If your old oscilloscope broke down and deemed beyond repair, you probably want to replace it. You will find out that modern DSO’s (Digital Storage Oscilloscopes) can do much more than classic, cathode-ray models. One of the many new and exciting functions is FFT, a feature I immediately checked out when I purchased my Atten ADS-1102CAL. A review of my model can be found here.

FFT adds an extra dimension to the standard time domain: the frequency domain. All oscilloscope users are familiar with the time domain; just feed a waveform into your scope and the display will show shape and voltage over time:

ADS00003The frequency domain on the other hand shows what voltage is present at each frequency and will produce a screen we know from the spectrum analyzer:

GT-3-UHF2Some measurements which are very hard in the time domain are very easy in the frequency domain. Consider the measurement of harmonic distortion. It’s hard to quantify the distortion of a sine wave by looking at the signal on an oscilloscope. When the same signal is displayed on a spectrum analyzer, the harmonic frequencies and amplitudes are displayed with pinpoint precision.

Another example is noise analysis. Looking at an amplifier’s output noise on an oscilloscope basically measures just the total noise amplitude. On a spectrum analyzer, the noise as a function of frequency is displayed. It may be that the amplifier has a problem only over certain frequency ranges. In the time domain it would be impossible to tell.

Most modern DSO’s, even the affordable models made by Atten and Rigol, are capable displaying both the time- and the frequency domain, and can do so at the same time. The time domain will be displayed at the upper half of the screen, the frequency domain at the lower half of the screen.

Atten-FFTWhile FFT on a DSO is not as accurate as a real spectrum analyzer (especially when reaching the upper limit of the scope’s bandwidth), it will give you a reasonably good idea of what’s happening.

How FFT works
If you’re new to FFT, your head might explode while trying to get a grip on it. I still struggle with it.

Fourier’s theorem: any waveform in the time domain can be represented by the weighted sum of sines and cosines. The FFT software samples the input signal, computes the magnitude of its sine and cosine components, and displays the spectrum of these measured frequency components.

Got it in one go? I didn’t when I tried it for the first time. Yesterday I ran into this website, which will be of some help.

fourierYou can see this in a simulation when you click here: http://hascanvas.com/fftvisualize2

The guys from Tektronix made a nice YouTube video which explains a lot too.

: do not connect your FFT capable DSO to whatever transceiver without proper external attenuation. Check the manual for maximum input level (often referred to as ‘damage level’) before measuring.

Feed the DSO with as little power as you can get away with. This will prevent overloading the DSO’s circuits and will result in more accurate measurements.

Have fun!

Some updates

Due to family matters it’s been a bit hectic here, and some plans had to be put on ice for a while. This is what happened in the mean time:

  1. I ordered a Rigol DSA-815TG. ETA is tomorrow, or next Monday. Can’t wait. I started assembling cables and constructing  a 15 – 45dB external attenuator in advance.
  2. Next Monday (September 10) I will get three Wouxun radios for review, including the KG-UV920R. Many thanks to Ruud from Bamiporto.nl, who runs the place.
  3. I’m thinking of destroying my BlackBerry with a hammer and replace it by something Samsung.
  4. I almost finished assembling the receiving part of a remote control for our regional 70cm repeater.

P.S. Some dogs are real losers.